Part 3-Motion in a plane hard

A soldier jumps out from an aeroplane with a parachute. After dropping through a distance of 19.6 m, he opens the parachute and decelerates at the rate of 1 ms^-2. If he reaches the ground with a speed of 4.6 ms^-1, how long was he in air?

A car is travelling at a velocity of 10 kmh^-1 on a straight road. The driver of car throws a parcel with a velocity of 10√2 kmh^-1 when car is passing by a man standing on the side of a road. If parcel just reaches the man, the direction of throw makes following angle with the direction of car

A particle starts from the origin of coordinates at time t= 0 and moves in the xyplane with a constant acceleration a in the y-direction. Its equation of motion is y = βx². Its velocity component in the x- direction is

A fighter plane is pulling out for a dive at 900 km/h in a vertical circle of radius 2km. Its mass is 5000 kg. Find the force exerted by the air on it at the lowest point

A car is moving on a horizontal circular road of radius 100 m with a uniform speed 10 ms^-1. It suddenly accelerates at 1 ms^-2. The acceleration is

A spotlight is fixed 4 m from the vertical wall and is rotating at a rate 1 rads^-1. The spot moves horizontally on the wall. Find the speed of the spot on the wall when the spotlight makes an angle of 45^o with the wall.

A string of length 1m is fixed at one end and carries a mass of 100 g at the other end. The string makes 2/p revolutions per second around the vertical axis through the fixed end. If angle of inclination of the string with the vertical is cos^-15/8, the linear velocity of the mass is nearly

A car is moving on a circular horizontal track of radius 10m with a constant speed of 10 ms^-1. A plumb bob is suspended from the roof of the car by a light rigid rod of length 10 m. The angle made by the rod with the track is

A particle moves in a circular path of radius r with speed v. It then increases its speed to 2v while traveling along the same circular path. The centripetal acceleration of the particle has changed by a factor of –

A particle is tied to a light inextensible string of length L and whirled in a vertical circle with other end of string as centre. At a certain instant when the string makes angle θ= 53ۜ° with lower vertical its speed is found to be v =√5gL , then its acceleration at that instant of time is –

A pendulum consisting of a small sphere of mass M suspended by an inextensible and mass less string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2Mg, then the maximum angular amplitude of the displacement form the vertical can be -

A particle of mass m revolves in a circle of radius r with a uniform speed n, then its velocity vector -

A body is moving in a circle at a uniform speed n. What is the magnitude of the change in velocity when the radius vector describes an angle θ ?

A car is travelling along a circular curve that has a radius of 8m. If its speed is 8 m/s and is increasing uniformly at 8 m/s², the magnitude of its acceleration at this instant is -

A simple pendulum of length  and mass m is initially at its lowest position. It is given the minimum horizontal speed necessary to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is-

A small particle of mass 0.36 g rest on a horizontal turntable at a distance 25 cm from the axis of spindle. The turntable is accelerated at a rate of a = 1/3 rad/s^–2. The frictional force that the table exerts on the particle 2 s after the startup is-

Two particles starting from a point on a circle of radius 4 m in horizontal plane move along the circle with constant speeds of 4 ms^–1 and 6 ms^–1 respectively in opposite directions. The particles will collide with each other after a time of :

119. A non-uniform thin rod of length L is placed along x-axis as such its one of ends is at the origin. The linear mass density of rod is λ = λ₀xThe distance of centre of mass of rod from the origin is :

An aeroplane is moving in a circular path with a speed 250 km/hr; what is the change in velocity in half revolution -

A constant torque acting on a uniform circular wheel changes its angular momentum from A₀ to 4A₀ in 4 seconds. The magnitude of this torque is

In a simple pendulum, the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle θ with the vertical-

A ball is projected with velocity u at an angle α with horizontal plane. Its speed when it makes an angle β with the horizontal is –